a 9 pt SUN to the MasteringPhysics website. 10. (II) A bucket of mass 2.00 kg is

Question

a 9 pt SUN to the MasteringPhysics website. 10. (II) A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.20 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N. (a) Find the speed of the bucket. (b) How fast must the bucket move at the top of the circle so that the rope does not go slack? 11. (II) How many revolutions per minute would a 25-m- diameter Ferris wheel need to make for the passengers to feel "weightless" at the topmost point? 12. (II) A jet pilot takes his aircraft in a vertical loop (Fig.5-38). (a) If the jet is moving at a speed of 840 km/h at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0g's. (b) Cal- culate the 78-kg pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle, and (c) at the top of the circle (assume the same speed). FIGURE 5-38 Problem 12. 13. (II) A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire), Fig. 5-39. The circle formed by

Explanation / Answer

11)

At the top of the ferris wheel, newtons second law tells you

normal force acting on person - weight = centrip force

since the centrip force acts toward the center of the wheel, the direction of the force is down (in the same direction as weight), so our equation becomes:

N - mg = -mv^2/r or N=mg-mv^2/r

you will feel weightless when N=0, or when mg = mv^2/r, or when

v = sqrt(gr)

for a 25 m diameter ferris wheel, the radius is 12.5m speed is sqrt(12.5x9.8) = 11.068 m/s

Circumference = 2r = = 78.54 m per rev

At 11.068 m/s it takes

11.068m/s / 78.54m = 0.1409 rev/sec x 60s/m = 8.46 rev/min

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